Introduction to phase transitions. Ising model and related models. Mean field. Critical exponents. Landau theory. Variational approaches. Correlation functions. Coarse-graining and scaling. Renormalization group equations. Fixed points and universality. Scaling laws and critical exponents. Renormalization group in real space and momentum space. Continuum limit and field theories. Symmetries and their breaking. Goldstone modes. Topological defects. Exact models. XY model.
H. Nishimori, G. Ortiz, “Elements of phase transitions and critical phenomena”
S. Blundell, “Magnetism in condensed matter”
J.M. Yeomans, “Statistical mechanics of phase transitions”
P.M. Chaikin and T.C. Lubensky, “Principles of condensed matter physics”
H.E. Stanley, “Introduction to phase transition and critical phenomena”
Learning Objectives
The student is called upon to understand and master theoretical knowledge and methodologies to study phase transitions and critical phenomena. These include mean-field theory, the renormalization group, Kosterlitz-Thouless transition and exact solutions too. In general, the student will acquire the skills to be able to investigate critical phenomena in different frameworks of theoretical physics (condensed matter, complex systems and high energy physics).
Prerequisites
Bachelor's degree courses in physics.
Teaching Methods
Number of hours related to classroom activities: 48
Type of Assessment
The exam consists of an oral test. During the test, the student is called to present 2 or 3 topics related to the program. The oral test takes place at the blackboard and lasts about 60 minutes.
Course program
Introduction to phase transitions. Ising model and related models. Mean field. Critical exponents. Landau theory. Variational approaches. Correlation functions. Coarse-graining and scaling. Renormalization group equations. Fixed points and universality. Scaling laws and critical exponents. Renormalization group in real space and momentum space. Continuum limit and field theories. Symmetries and their breaking. Goldstone modes. Topological defects. Exact models. XY model.